What is the possible value of (a + b + c) – 3 , if a2 + b2 + c2 = 9 and ab + bc + ca = 8?

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SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 4)
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  1. 5
  2. 3
  3. 9
  4. 2

Answer (Detailed Solution Below)

Option 4 : 2
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Detailed Solution

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Given:

a2 + b2 + c2 = 9 and ab + bc + ca = 8

Concept used:

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

Calculation:

(a + b + c)2 = 9 + 2 × 8

⇒ 9 + 16

⇒ 25

So, (a + b + c ) = 5

Now,

(a + b + c) – 3 = 5 - 3

⇒ 2

∴ The required answer is 2.

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